Climate change is one of the biggest challenges of this time. One of the necessary changes to combat this challenge is a shift from conventional power resources, such as coal and natural gas, to large scale deployment of renewable resources, such as wind and solar power. However, renewable energy resources are volatile because they depend on the weather, which poses a problem because supply and demand should always be exactly matched. Along with a shift in energy production, also appliances that use non renewable energy are becoming electric, e.g., electric heating and cooling in buildings and electric vehicles. This causes an increase in electricity demand and is a burden on the main grid. To reduce the demand on the grid, it is important that a part of the energy is produced locally by distributed renewable resources, such as residential solar panels. To maintain a stable operation of the grid, the smart grid paradigm has to be adopted. Advancements in information and communication technologies provide the means for an efficient management of the grid using various services, such as distributed generation and storage. Because of the conflicting nature of the agents in an electricity network, game theory is a widely used framework to tackle this problem. In a realistic model of a power grid coupling constraints must be taken into account, because the agents have shared resources. Therefore, the economic dispatch problem is modeled as a noncooperative game with coupling constraints, called a generalized game. Three distributed algorithms are derived to reach a generalized Nash equilibrium. It is shown through simulations that these algorithms have the potential to ensure a safe and efficient operation of the grid, while minimizing the cost of power usage. To reduce the cost even further, a method is presented to make more optimal use of the storage units.